Mr Robert’s grandfather was 99 year old when he died. Evaluate the cube of his age using suitable formula.
Answers
Given,
Age of the grandfather = 99
To find,
The cube of the age of the grandfather by using one of the given formula.
Solution,
We can use the formula of the (x-y)³ to solve this mathematical problem.
For this, we have to break the given numerical value into the subtraction of two perfectly cube numbers.
99 = 100-1
(Both, 100 and 1 are perfectly cube)
Let,
x = 100
y = 1
(x-y)³
= x³-y³-3xy(x-y)
= (100)³-(1)³- 3×100×1×(100-1)
= 1000000-1-300×99
= 1000000-1-29700
= 1000000-29701
= 970299
or, = (99)³
Hence, the cube of the age of the grandfather is 970299
Given,
Volume of the cube = 8x³-36x²+54x-27
To find,
Expression for each side of the cube.
Solution,
Let, the side of the cube = a
(Assume, "a" as the variable to do the further mathematical calculations.)
Volume of the cube = a³
According to the data mentioned in the question,
a³ = 8x³-36x²+54x-27
a³ = 8x³-27-36x²+54x
a³ = (2x)³-(3)³- 3×(2x)²×3 + 3×2x×(3)²
a³ = (2x-3)³
a = 2x-3
Hence, the expression of one side of the cube is (2x-3).
Answer:
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